Three-dimensional instability of a ow past a sphere: Mach evolution of the regular and Hopf bifurcations
| Autor: | Andrea Sansica, Frédéric Alizard, Eric Goncalves, J.-Ch. Robinet |
|---|---|
| Přispěvatelé: | Centre National d'Études Spatiales [Toulouse] (CNES), Laboratoire de Dynamique des Fluides (DynFluid), Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Institut Pprime (PPRIME), ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers, Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Wake
Sciences de l'ingénieur 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics symbols.namesake [SPI]Engineering Sciences [physics] Bifurcation Compressible flows Chock waves 0103 physical sciences Supersonic speed 010306 general physics Bifurcation Hopf bifurcation Physics Shock (fluid dynamics) Mechanical Engineering Reynolds number Mechanics Condensed Matter Physics Mach number Flow (mathematics) Mechanics of Materials symbols Compressible flows Chock waves |
| Zdroj: | Journal of Fluid Mechanics Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 855, pp.1088-1115. ⟨10.1017/jfm.2018.664⟩ |
| ISSN: | 0022-1120 1469-7645 |
| Popis: | A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics. |
| Databáze: | OpenAIRE |
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